If $x \veebar y = 2x^{2}-y^{2}$ and $x \bigtriangleup y = (3-x)(y)$, find $-6 \veebar (1 \bigtriangleup -4)$.
Answer: First, find $1 \bigtriangleup -4$ $ 1 \bigtriangleup -4 = (3-1)(-4)$ $ \hphantom{1 \bigtriangleup -4} = -8$ Now, find $-6 \veebar -8$ $ -6 \veebar -8 = 2(-6)^{2}-(-8)^{2}$ $ \hphantom{-6 \veebar -8} = 8$.